### Abstract

We provide optimal parameter estimates and a priori error bounds for symmetric discontinuous Galerkin (DG) discretisations of the second-order indefinite time-harmonic Maxwell equations. More specifically, we consider two variations of symmetric DG methods: the interior penalty DG (IP-DG) method and one that makes use of the local lifting operator in the flux formulation. As a novelty, our parameter estimates and error bounds are $i)$ valid in the pre-asymptotic regime; $ii)$ solely depend on the geometry and the polynomial order; and $iii)$ are free of unspecified constants. Such estimates are particularly important in three-dimensional (3D) simulations because in practice many 3D computations occur in the pre-asymptotic regime. Therefore, it is vital that our numerical experiments that accompany the theoretical results are also in 3D. They are carried out on tetrahedral meshes with high-order ($p = 1, 2, 3, 4$) hierarchic $H(\mathrm{curl})$-conforming polynomial basis functions.

Original language | Undefined |
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Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Number of pages | 34 |

Publication status | Published - Jan 2010 |

### Publication series

Name | Memorandum / Department of Applied Mathematics |
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Publisher | Department of Applied Mathematics, University of Twente |

No. | 1914 |

ISSN (Print) | 1874-4850 |

ISSN (Electronic) | 1874-4850 |

### Keywords

- METIS-270717
- Numerical mathematics
- EWI-17325
- Electromagnetic waves
- MSC-00A72
- Scientific computation
- Finite Element Method
- IR-69763

## Cite this

Sarmany, D., Izsak, F., & van der Vegt, J. J. W. (2010).

*Optimal penalty parameters for symmetric discontinuous Galerkin discretisations of the time-harmonic Maxwell equations*. (Memorandum / Department of Applied Mathematics; No. 1914). Enschede: University of Twente, Department of Applied Mathematics.